Topological Ramsey spaces introduced by Todorcevic are spaces equipped with further structure (an ordering, a notion of approximation) which satisfy certain axioms. These spaces can be seen as abstract variations of the classical Ellentuck space and provide a unified framework for proving combinatorial partition theorems.

We introduce a new type of A topological Ramsey space consisting of certain strong (sub)trees, which can be can be used for coding rational countable pseudotrees.